Isomorphisms - PowerPoint PPT Presentation

Lecture 2: Introduction to Category Theory

Lecture 2: Introduction to Category Theory. Nick Rossiter, Computing Science, Newcastle University, England B.N.Rossiter@newcastle.ac.uk http://www.cs.ncl.ac.uk/people/b.n.rossiter/. Features of Interoperability. Complex mappings from user views to way data is held

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Chapter 3: Linear transformations

Chapter 3: Linear transformations. Linear transformations, Algebra of linear transformations, matrices, dual spaces, double duals. Linear transformations. V, W vector spaces with same fields F . Definition: T:V W s.t. T(ca+b)=c(Ta)+Tb for all a,b in V. c in F. Then T is linear.

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CHANGE OF BASES

CHANGE OF BASES. Arbitrary vector spaces are so … i t is not so easy to do any meaningful computa-tion in them. But, as we have seen, if we have a basis f or an arbitrary finite dimensional vector space V , then the coordinate mapping

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